This study aims to develop a mathematical model of a solar chimney considering air as a participatory medium for a rooftop solar chimney. Steady-state heat transfer equations were derived for glass, the air between glass and absorber plate and for absorber wall separately. These equations were then solved by the matrix method using the Gauss-Seidel iteration approach in the in-house developed MATLAB code. The in-house code was validated with simulation studies from the literature. Relative humidity quantifies the absorbing characteristic of humid air. Initially, to study the variation of the mass flow rate through the solar chimney as a function of relative humidity, heat transfer to air was considered to be via radiation alone to quantify the contribution from radiation alone by making convective heat transfer coefficients zero. There was a 10% to 12% increase in air flow rate with 50% relative humidity, compared to air with 10% relative humidity when the insolation varies between 500 W/m² to 750 W/m². Thus, moist-air as a participatory media should be considered while developing mathematical models. The developed mathematical model for solar chimney considering moist air as participating media (along with convection terms) and with turbulent co-relation for Nusselt number better predicted the overall result. And finally, the effect of absorptivity of absorber wall on the chimney performance is also presented.